The main ideas are introduced in a historical context. Beginning with phase retrieval and ending with neural networks, the reader will get a sense of the book’s broad scope.

There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like.

This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.

Newtons laws of motion are not the last word in classical mechanics. In the 250 years after Newton, physicists and mathematicians found ways to reformulate classical mechanics, providing powerful tools to solve problems but, equally as importantly, giving us a new perspective on the laws that govern our universe. This chapter takes the first step in this direction. We will introduce the wonderful principle of least action, a simple rule that underlies all known laws of physics. This will give us new insights, not least the wonderful Noethers theorem, relating symmetries to conservation laws.

Beginning with linear programming and ending with neural network training, this chapter features seven applications of the divide-and-concur approach to solving problems with RRR.

In 1925, as matrix mechanics was taking shape, Lucy Mensing (1901−1995), who earned her PhD with Lenz and Pauli in Hamburg, came to Göttingen as a postdoc. She was the first to apply matrix mechanics to diatomic molecules, using the new rules for the quantization of angular momentum. As a byproduct, she showed that orbital angular momentum can only take integer values. Impressed by this contribution, Pauli invited her to collaborate on the susceptibility of gases. She then went to Tübingen, where many of the spectroscopic data were obtained that drove the transition from the old to the new quantum theory. It is hard to imagine better places to be in those years for young quantum physicists trying to make a name for themselves. This chapter describes these promising early stages of Mensing’s career and asks why she gave it up three years in. We argue that it was not getting married and having children that forced Lucy Mensing, now Lucy Schütz, out of physics, but the other way around. Frustration about her own research in Tübingen and about the prevailing male-dominated climate in physics led her to choose family over career.

Over the past hundred years or so, physicists have developed a foolproof and powerful tool that allows us to understand everything and anything in the universe. You take the object that you’re interested in and you throw something at it. Ideally, you throw something at it really hard. This technique was developed around the turn of the 20th century and has since allowed us to understand everything from the structure of atoms, to the structure of materials, to the structure of DNA. In short, throwing stuff at other stuff is the single most important experi- mental method available to science. Because of this, it is given a respectable sounding name. We call it scattering.

The first four women to obtain a PhD in physics at Leiden University all graduated with Nobel laureate Hendrik Lorentz, among them Hendrika Johanna (Jo) van Leeuwen (1887−1974). She and her younger sister Cornelia (Nel) van Leeuwen finished their undergraduate studies in physics in Leiden in the early twentieth century. Whereas the younger sister left physics in 1917 after a relatively short period as a graduate student, Jo van Leeuwen went on to earn a PhD in 1919. Her thesis elucidates that magnetism is exclusively a quantum phenomenon – a result that was independently also obtained by Niels Bohr and that is now commonly known as the Bohr–van Leeuwen theorem. From 1920 onwards Van Leeuwen worked at the Technische Hoogeschool in Delft (now Delft University of Technology). Initially serving as an assistant, she was appointed as a reader in theoretical and applied physics in 1947, becoming the first female reader in Delft. This chapter outlines the foray into physics by the two sisters, focusing specifically on Jo van Leeuwen, detailing her work and early contributions to the quantum theory of magnetism.

In this chapter, we explore the concept of information in living organisms in its broadest sense. Biological organisms perceive the external environment, alter their own state, and take action (selection among possibilities). To capture these properties intrinsic to the organisms, we begin by discussing the “information quantity” that quantifies such situations. Starting with the definition of information quantity, we introduce Shannon entropy and provide an overview of Shannon’s information theory framework. We also discuss Kullback–Leibler divergence and mutual information. Next, moving on to information in DNA sequences, we cover various aspects such as differences in the frequency of AT and GC occurrence, the structure of genetic codes, long-range correlations in DNA sequences, and recent findings in intergenic sequences. Additionally, we explain kinetic proofreading as one candidate for achieving high accuracy in molecular recognition from a combination of unreliable elements. Furthermore, we explore the relationship between entropy in statistical mechanics and information, elucidating the connection between Maxwell’s demon and information using the Szilard engine as a mediator. Finally, we introduce intriguing points from the perspective of dynamics and information, highlighting the dynamic interplay between the two.

Chien-Shiung Wu (1912–1997) is often referred to as “the Chinese Marie Curie” even though she conducted most of her research in the US. She is best known for her discovery of the non-conservation of parity for weakly interacting particles – a finding for which she is widely regarded as having been passed over for the 1957 Nobel Prize in Physics. Seven years earlier, though, in a one-page letter to Physical Review, Wu and her graduate student also quietly reported what has come to be understood as the first conclusive evidence of entangled photons. Twenty years later, as quantum foundations research emerged from shadow, Wu revisited her 1949 experiment with a more refined approach. Wu shared the new results with Stuart Freedman, a collaborator of John Clauser. Clauser et al. would rigorously critique Wu’s experiments through at least 1978. In 2022, the Nobel Committee honored Clauser, Alain Aspect, and Anton Zeilinger, each of whom had produced increasingly convincing proof of entanglement beginning in the 1970s. Wu’s foundational work from almost seventy years earlier, however, was not mentioned. This chapter aims to help bring Wu’s entangled photons back into the light.